آداب معاشرت، سورة حجرات کی گیارهویں اور بارهویں آیات کے تناظر میں

Dr. Shari'ati is a revolutionary intellectual personality of this century. He regarded Islamic values ​​as the guarantee of salvation and success for humanity. He sought to mobilize and revive frozen Islamic ideas. That is, tried to bring the Islamic concept out of the boundaries of formal and congested boundaries into common and general thoughts. Dr. Shari'ati also presented a unique view that divine Imam transcends than worldly governments and this divine leadership cannot be determined by (Shuraiet). Rather, it can be diagnosed by an obvious reason (Nass). This doctrine of Dr. Shari'ati is contrary to the ideology of the Sunni and the Shi'ite’s concept of Imamat and Khilafat because the Sunni sect believes that Khilafat Or Imamt should be determine by the Shurait (Council) and Shiites by the will(Nass). According to Dr. Shairathi, Imamat cannot be determining through Shourait or Nass but it can be identified by the superior attributes of the Imam. He believes that Imamat is not an external factor which can gain by attainment or by choice; rather, it is an Inherit object.  In accepting this doctrine of Dr. Shari'ati, than the Imamat becomes a part of the system of naturalism (Takveeni). That makes the Imamat not a model process for humanity. So it would be a complicated issue to discuss and discover either the theory of Dr. Shari'ati is a applicable idea of Imamat or it is a just onlyu idialogy which cannot be practiced. The dissertation has been written to examine the reality of these two cases either Imamat is inherit case or it can be attainment case through Shouriat or Nass.   

Some Vertex-Degree-Based Topological Indices of Graphs

Many topological indices which are being used by researchers in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies to predict the physico-chemical properties of molecules, are based on vertex degrees of the corresponding molecular graphs. When a new topological index is introduced in chemical graph theory, one of the important questions that need to be answered is for which members of a certain class of n-vertex graphs this index assumes minimal and maximal values? On the other hand, there are many well known graph families and vertex-degree-based topological indices in the literature for which this question remains open. The main purpose of current study is to address this open question for some well known families of graphs. Firstly, the collection of all k-polygonal chains (for k = 3, 4, 5) with fixed number of k-polygons is considered and the extremal elements from this family are characterized with respect to several well known bond incident degree (BID) indices (BID indices form a subclass of the class of all vertex-degree-based topological indices). From the derived results, many already reported results are obtained as corollaries. Furthermore, the extremal 4-polygonal (polyomino) chains for some renowned vertex-degree-based topological indices (other than BID indices) are also determined. Next, the problem of characterizing the extremal cacti over the certain classes of cacti (tree-like polyphenylene systems, spiro hexagonal systems and general cacti) with some fixed parameters is addressed for various well known vertex-degree-based topological indices. Finally, some mathematical properties of the atom-bond connectivity index and augmented Zagreb index are explored